A270343 Numbers k that end with ( sum of digits of k )^2.

0, 1, 81, 3144, 3256, 6225, 6484, 6576, 7121, 7529, 7676, 9100, 9324, 9361, 9729, 9784, 12144, 12256, 15225, 15484, 15576, 16121, 16529, 16676, 18100, 18324, 18361, 18729, 18784, 21144, 21256, 24225, 24484, 24576, 25121

Offset: 1

Author

Soumil Mandal, Mar 15 2016

Keywords

• base
• nonn
• easy

Comments

All terms end with a digit from the set S = {0,1,4,5,6,9}.

The sum of the digits of the numbers repeat and also change with regular intervals. For example, the sum of the digits S1 = {12,16,15,22,24,11,23,26,10,18,19,27,28} which is followed by 3144 to 8784, 12144 to 18784, 21144 to 27784, 30144 to 36784. Again S2 = {21,25,15,22,24,11,23,26,10,18,19,27,28} is followed by 39441 to 45784, 48441 to 54784, 57441 to 67784, 66441 to 72784. It can be seen that a set containing 13 elements repeats itself for 4 consecutive ranges.

Examples

			For k=3256, sum of digits is 16 and 16^2 is 256.
For k=7121, sum of digits is 11 and 11^2 is 121.
For k=18784, sum of digits is 22 and 22^2 is 484.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000
• Soumil Mandal, Graph Of Sum Of Digits
• Soumil Mandal, Graph Of Cumulative Sums

Crossrefs

Cf. A003226, A008851, A018247, A118881.

Programs

Mathematica

Select[Range[0, 20000], Function[n, Function[k, If[n >= k, FromDigits@ Take[#, -IntegerLength@ k] == k, False]][Total[#]^2] &@ IntegerDigits@ n]] (* Michael De Vlieger, Mar 15 2016 *)
esdQ[n_]:=Module[{idn=IntegerDigits[n],idn2=IntegerDigits[ Total[ IntegerDigits[ n]]^2]},Take[ idn,-Length[idn2]]==idn2]; Select[ Range[ 0,26000],esdQ]//Quiet (* Harvey P. Dale, Jan 01 2022 *)

PARI

isok(n) = {sds = sumdigits(n)^2; nbs = #Str(sds); ((n - sds) % 10^nbs) == 0;} \\ Michel Marcus, Mar 16 2016

Python

for i in range(0,200000):
    res = pow((sum(map(int,str(i)))),2)
    if(i%pow(10,len(str(res)))==res):print(i)
# Soumil Mandal, Mar 17 2016